I think the crux of the “Cooper” case is that the OC must demonstrate actual, real world, interference with the amenity of other residents. In other words, by-laws that ban any pets because they might create a problem are invalid. But pet by-laws that allow for the removal of pets that actually do create a problem are valid.
So, if you keep a pet, and then the OC takes action to uphold their by-law against you, they will fail unless they have evidence that your pet is creating a real world nuisance.
The argument that some other owners don’t like pets, or that pets are dirty would not hold up, without evidence that an owner is terrified of dogs (say) or that your pet pooped on the front lawn of the building (say). Even then, the nuisance has to be a reasonable one. A one-off incident probably would not count, and they would need evidence of a persistent problem.
In the decision from @TheHood the key terms are “actual unreasonable interference” and “a particular animal in the absence of satisfactory evidence of unreasonable interference by that animal with neighbourhood amenity”. I’m not sure what the case was about exactly (maybe provide a copy of the decision?), but if it was just to invalidate the pet by-law, I can understand why that lost.
An OC may have a by-law that allows pets to be removed. But they can only do that for a specific pet, for specific reasons based on clear evidence of mischief, that interferes with at least one other resident’s enjoyment of their property, with evidence of that required.
And the only way that can work, is for the pet to be in residence in the building already. So a pets by-law generally can’t easily prevent a pet being kept on the property initially, but once it is there, if it makes a nuisance of itself, then the by-law can allow for its removal.
An exception is where any pet coming on to the property must always create a nuisance – eg large dogs in a building designed for elderly or infirm residents, or cats in buildings that are havens for native birds or beside a national park.